Properties

Label 189.1.m
Level $189$
Weight $1$
Character orbit 189.m
Rep. character $\chi_{189}(82,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 189.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(189, [\chi])\).

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q + q^{4} - 2q^{7} + O(q^{10}) \) \( 2q + q^{4} - 2q^{7} - q^{16} - q^{25} - q^{28} - 3q^{31} - q^{37} + 2q^{43} + 2q^{49} + 3q^{52} + 3q^{61} - 2q^{64} + q^{67} + q^{79} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(189, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
189.1.m.a \(2\) \(0.094\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{6}q^{4}-q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+\cdots\)